Definitively yes. Capturing he moment, taking pictures, can be part of this moment, especially when you feel inspired, but they are not all the moment.
I very often drop the camera to better "live the moment". It might be before starting to shoot, or in the middle of the shooting, or even near the end. It helps me have a better feeling of what I have in front of me, place, landscape, animal or people, and doing so I totally forgot the camera for a few minutes. Then I usually take the camera back and go for new, more inspired compositions.
I may miss some pictures but seldom feel bad for enjoying the moment instead of capturing it, whereas I always feel bad when I take picture while feeling "outside the moment" because I missed it and my pictures are usually bad.